use the law of sines to find the indicated side length in this triangle. round your answer to the nearest…

Explanation:

Step1: Recall the law of sines

The law of sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ for a triangle with sides $a$, $b$, $c$ and opposite - angles $A$, $B$, $C$ respectively. Let the side of length $15$ be opposite the $61^{\circ}$ angle and the unknown side be opposite the $70^{\circ}$ angle.

Step2: Set up the proportion

We have $\frac{x}{\sin70^{\circ}}=\frac{15}{\sin61^{\circ}}$, where $x$ is the unknown side length.

Step3: Solve for $x$

Cross - multiply to get $x=\frac{15\sin70^{\circ}}{\sin61^{\circ}}$. We know that $\sin70^{\circ}\approx0.9397$ and $\sin61^{\circ}\approx0.8746$. Then $x = \frac{15\times0.9397}{0.8746}=\frac{14.0955}{0.8746}\approx16.12$.

Answer:

$16.12$